For another common concern on the relationship between our dual framework presented in this paper and Dung's argumentation theory [1]}, as we have foretold in Section , Dung's arguments seem to attack each other only in the weak sense, because accordingly in his definition of consistency, any two arguments in a consistent set can never attack one another, which seems to be even stricter than our later definition in Section  of maximal consistent sets of arguments as ultrafilters over a preorder. Anyway, although Dung's definition is perhaps not strong enough to fulfill our demand here as a dual theory, we might still consider using it in certain due case.
